The US Secretary of State would like the forces to oversee humanitarian efforts, enforce a ceasefire and no–fly zones.
Mr Tillerson, in a statement ahead of this week’s G20 summit in Germany, said: “If our two countries work together to establish stability on the ground, it will lay a foundation for progress on the settlement of Syria’s political future.”
The US Secretary of State said the volatile situation in Syria would be a topic of discussion between President Donald Trump and Russia ‘s Vladimir Putin.
The two country’s have clashed repeatedly over Moscow’s support for the Syrian president Bashar al–assad, who the US believe has used chemical weapons against his own people.
Mr Tillerson added: “Russia, as a guarantor of the Assad regime and an early entrant into the Syrian conflict, has a responsibility to ensure that the needs of the Syrian people are met and that no faction in Syria illegitimately re-takes or occupies areas liberated from ISIS’ or other terrorist groups’ control.”
In April the US launched 59 Tomahawk cruise missiles targeting an airbase from which White House officials said the Syrian regime had launched a chemical weapons attack on civilians.
Assad is still in power thanks to Russia’s support which has helped the Syrian Government turn the tide in a multi-sided war against ISIS and rebels.
US national security adviser H R McMaster told reporters ahead of the G20 summit that Mr Trump “will lay out a vision not only for America’s future relationship with Europe, but the future of our trans-Atlantic alliance, and what that means for American security and American prosperity”.
Aside from shoring up the US relationship with Nato allies, the speech is symbolic given Poland’s proximity to Russia and regional fears about Moscow’s ambitions following its 2014 annexation of Crimea from Ukraine.
It will be a busy trip for Mr Trump as he will also be meeting Chinese president Xi Jinping, with whom he has expressed some frustration for failing to use enough leverage to curb North Korea’s nuclear program.
Pyongyang said on Tuesday it successfully test-launched a newly developed intercontinental ballistic missile, which analysts said could put all of the US state of Alaska in range for the first time.
Mr Trump arrived in Poland last night ahead of the G20 summit in Hamburg, Germany.